I'm planning to order MDCK-MRP1 overexpressing cell lines. I have checked 10 references and all of them used DMEM(with L-glutamine) +10% FBS+ 1% of non-essential amino acids. As a matter that I'm quite new to this cell lines (MDCK), therefore any helpful comments are highly appreciated.

The differences that I notice are:
1. The concentration of Penicillin/Streptomycin that the majority use
2% of them but 2 papers use 1%.
2. One paper mention that they add 1% amphotericin B as an antifungal.

As a routine practice you should not be using antibiotics in your cell culture, it masks cryptic infections of common bacteria such as E. coli which can have a major effect on your cells, including such things as protein expression, attachment and cell signalling. You should also routinely test your cells for mycoplasma.

MDCK should be fine in DMEM with 10% FBS, though the ATCC has the following to say:

ATCC complete growth medium: The base medium for this cell line is ATCC-formulated Eagle's Minimum Essential Medium, Catalog No. 30-2003. To make the complete growth medium, add the following components to the base medium: fetal bovine serum to a final concentration of 10%.Atmosphere: air, 95%; carbon dioxide (CO2), 5%Temperature: 37.0°C

If you got them from the ATCC you should be growing them in their suggested medium or weaning them onto DMEM if you prefer. IF the people in your lab have already weaned them onto DMEM they should be fine.